"I died on 6-4." "I got the Orange Portal Gun." That's what separates games from movies and, to me, makes them more fulfilling. It's not Mario who you say died.
You died. Bonus comedy: The one who entered as Zero Suit Samus is a dude and the one who entered as Ike is not.
If you don't like self-insertion, don't worry--I don't intend to do it very often. If you do like self-insertion, do worry--I don't intend to do it very often.